The sample space of a random experiment is left-brace a comma b comma c comma d

Question

The sample space of a random experiment is left-brace a comma b comma c comma d comma e comma f right-brace , and each outcome is equally likely. A random variable is defined as follows: outcome a b c d e f x 0 0 9.3 9.3 14 18 Determine the probability mass function of . Use the probability mass function to determine the following probabilities: [Give exact answers in form of fraction.] (a) Upper P left-parenthesis Upper X equals 9.3right-parenthesis equals (b) Upper P left-parenthesis 2.9less-than Upper X less-than 16.4right-parenthesis equals (c) Upper P left-parenthesis Upper X greater-than 18right-parenthesis equals (d) Upper P left-parenthesis 0 less-than-or-equal-to Upper X less-than 14right-parenthesis equals (e) Upper P left-parenthesis Upper X equals 0 or Upper X equals 14right-parenthesis equals

Explanation / Answer

outcome

X

probability

0

1/6

0

1/6

9.3

1/6

9.3

1/6

14

1/6

18

1/6

Probability Mass Function PMF :

a) P(X=9.3) =2/6=0.5

b) P(29<X<18)=P(x<18)-P(X<2.9)

=2/6+2/6+1/6-2/6

=5/6-2/6=3/6=0.5

c)P(X>18)=1-P(X<=18)=1-1=0

d)P(0<=X<14)=P(X<14)-P(X<=0)

=4/6=06667

e)

outcome

X

probability

0

1/6

0

1/6

9.3

1/6

9.3

1/6

14

1/6

18

1/6

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